Hydrology Predicts How Many Subsidence Claims Reach Insurers in the Water Allocation Zones but Not How Large They Are: Evidence from Four Insurers, DE 31–54

1. Introduction

Across the 96 communes of the Trisolaran Crisis Water Allocation Zones, four insurers paid 57,823 subsidence claims between DE 31 and DE 54, and every one of them fell inside one of 806 commune-years, out of a possible 2,304, in which the Water Allocation Secretariat of the UN Planetary Defense Council (PDC), whose records we use, had declared a "disaster area". In the remaining 1,498 commune-years the compulsory cover paid nothing, and in the declared ones the median declared commune-year held 64 claims.

We write in Deterrence Era, Year 57, at a point when the slow costs of the Crisis-Era water allocations are reaching the ledgers of the insurers. The dwellings of the zones, a large share of them built on shallow footings, stand on clays that shrink as the water table falls, and the subsidence cover which the PDC imposed on every household is the only channel through which that shrinkage is priced (PDC Water Allocation Secretariat, 27 DE).

The mechanism itself has been described. Tosun and Valderrama (41 DE) documented cracking in shallow-footed masonry on expansive clay, and Eskildsen (46 DE) tied the drawdown below the Three Gorges reservoir to the shrink-swell cycle of the middle-reach clays. Similarly, Maruyama (50 DE) levelled 1,100 dwellings in one zone and found settlement concentrated in the dry months. And in the actuarial literature, Lindqvist and Okoro (49 DE) fitted hurdle models to catastrophe-cover claims, and Ferreira and Dlamini (52 DE) found the Secretariat's declarations tracked its political priorities as well as the gauge record.

In order to apprehend how far one year's hydrology fixes the next year's losses, we will study the claims paid by four insurers, anonymised in the register as Insurers A to D, and we build a drought index from the gauge and allocation records of the zones. Frequency and severity are modelled separately, namely as a count of claims per commune-year and as the average amount paid per claim. The aim is to settle whether one year's hydrology predicts the next year's claims, in number and in size. The practical stake is the subsidence reserve that the Secretariat now requires of insurers (Sorokowski, 55 DE).

The answer for frequency is yes, with reservations. The answer for severity is no.

2. Methods

The register holds annual claim counts and paid amounts by commune for DE 31–54, in constant DE 31 yuan, from four insurers which together held roughly one third of household policies under the compulsory cover. It covers 96 communes in six zones of 16 communes each, with 508,890 insured households in DE 31 and 802,474 in DE 54, a mean of 6,719 per commune-year. Claims were booked by year and not by month. The cover pays only in a commune that the Secretariat has declared a "disaster area" for that year, and the declaration is issued after the year closes (PDC Water Allocation Secretariat, 55 DE), so the filter sets a commune-year's count to zero before any hydrology acts on it.

Hydrology enters through a drought index that we constructed for this study (the standardized allocation-deficit index – SADI). For each commune-year we took the gap between the volume scheduled for the zone and the volume gauged at the commune's nearest station, divided it by the scheduled volume, and standardised the result against all 2,496 commune-years of DE 29–54, so that +1 is one standard deviation drier than the mean of that period. The two years before the claims window supply the lags of the first two claim years. Every predictor for year t uses hydrology no later than year t-1.

Claim frequency was modelled with a zero-inflated Poisson regression (ZIP) with an offset for the log of insured households, and the count part used the mean SADI of years t-1 and t-2, the share of insured stock standing on clay and a building-age index. The zero part, which stands for the declaration filter, used the SADI of year t-1 and a fixed zone score for declaration priority taken from the Secretariat's allocation schedule.

Severity, the average amount paid per claim in a commune-year, exists only where claims exist. We fitted a bagged ensemble of 60 regression trees of depth four with a minimum leaf of 25 (a random forest without feature subsampling) on the commune's mean severity in the training years, clay share, building age, calendar year, zone and two hydrology inputs and one declaration flag, namely the SADI of year t-1, the mean SADI of years t-1 and t-2, and whether the commune was declared in t-1. Two comparison forests were fitted, one without the hydrology inputs and one given only the hydrology and declaration inputs (Rahimi, 38 DE). A benchmark with no model at all took each commune's mean severity in the training years as the prediction.

All models were fitted on DE 31–46 (1,536 commune-years, 41,827 claims, 589 commune-years with claims) and scored on DE 47–54 (768 commune-years, 15,996 claims, 217 commune-years with claims). Frequency was scored by the reduction in Poisson deviance against each commune's own training claim rate, and by the Spearman correlation between predicted and observed claims per 1,000 households across the 48 zone-year cells. Severity was scored by R² against the training mean. Intervals for frequency come from 200 bootstrap resamples of communes with refitting, and intervals for severity from 1,000 resamples of the held-out commune-years.

3. Results

The declaration filter is large, since declared commune-years made up 35.0% of the panel and the declared share rose from 22.9% in the least declared zone to 46.4% in the most declared. Observed claims averaged 3.74 per 1,000 insured households over the whole panel and 10.86 per 1,000 in declared commune-years alone. The SADI of consecutive years was correlated at 0.60, which is what allows last year's hydrology to say anything about this year's claims.

On the held-out years, the ZIP model with lagged SADI reduced the Poisson deviance by 26.0% against the commune-rate baseline (95% CI 21.4 to 30.6). The same model without hydrology reduced it by 4.8%, and predicted claims in DE 47–54 exceeded the observed total by 0.8%. Each standard deviation of the lagged SADI multiplied the expected count in a declared commune-year by 1.39 (95% CI 1.35 to 1.43), and across the 48 zone-year cells the predicted and observed claim rates had a Spearman correlation of 0.78 (95% CI 0.67 to 0.84), against 0.28 (95% CI 0.01 to 0.54) for the model without hydrology.

Ranking communes within a year went poorly. The pooled Spearman correlation over the 768 held-out commune-years was 0.13, the yearly values ran from -0.26 to 0.21. And the zero part of the model separated declared from undeclared commune-years with an area under the curve of 0.69.

For severity the picture is the opposite. Among the 217 held-out commune-years with claims, the forest that included the hydrology and declaration inputs reached an R² of 0.408 (95% CI 0.243 to 0.532), and the forest without any hydrology input reached 0.404. The increment from those inputs was 0.004 (95% CI -0.009 to 0.022). The forest given only the hydrology and declaration inputs scored -0.082 (95% CI -0.119 to -0.044), below the training mean, and its predictions were negatively correlated with the outcome (r = -0.16). Permutation of each of the two hydrology inputs and the declaration flag changed the full forest's R² by less than 0.002 in absolute value.

The commune's own history carried the severity forecast.

A prediction equal to each commune's mean severity in the training years, with no model at all, scored an R² of 0.412 (95% CI 0.261 to 0.533) on the same 217 commune-years. Across commune-years the average claim was 33,569 yuan, with a standard deviation of 9,696 yuan.

4. Discussion

Claim frequency is predicted reasonably well at the level where reserves are set, namely the zone-year, and hydrology is what predicts it: removing the SADI inputs cut the deviance reduction from 26.0% to 4.8%.

The proposition that next year's claim severity can be predicted from this year's hydrology is not supported by these data. Adding two hydrology inputs and a declaration flag to the severity forest changed its R² by 0.004, and a forest given only those inputs did worse than the training mean. The average claim is carried by the commune's own record of average claims.

Declarations limit what the frequency result means. A commune-year enters the ledger only after a declaration, and the declared share differed by a factor of two between the least and most declared zones even though the zone score for declaration priority was in the model. The zero part reached an area under the curve of 0.69, so most of the variation in declarations is unexplained by anything we hold, and part of it may be political, as Ferreira and Dlamini (52 DE) found for earlier years. A forecast of frequency is therefore a joint forecast of the soil and of the Secretariat.

We write within the Luo-Ji / Ye framework, in which the fixed arrival date of the Trisolaran fleet sets the planning horizon for slow risks; a peril whose frequency follows the allocation deficit one to two years earlier can be provisioned a year ahead, and a peril whose size hydrology does not help to forecast is reserved at the commune's own historical average.

For the reserve this means that the frequency model fixes the number of claims to be provisioned, and severity is provisioned at each commune's own average. How far the same declaration filter distorts the loss records of other slow perils under compulsory cover, such as river-bank erosion, is a methodological question for the Secretariat's actuaries that the claims of one peril cannot settle.

5. Limitations

The best frequency model still cannot say which communes will be declared in a given year. Its within-year ranking correlation of 0.13 is close to nothing, and the zone-year result of 0.78 shows only that the model follows the large movements between zones and years.

Held-out years were wetter than the training years, with a mean SADI of -0.39 against 0.06, and claims fell from 4.41 to 2.67 per 1,000 households between the two periods. A longer record containing a second drought would test the frequency model more severely than eight years of recovery can.

No record gave footing depth, plot gradient or nearby trees for any property, and claims were booked by year, so no seasonal indicator could be built even though cracking concentrates in the dry months (Maruyama, 50 DE). The severity test covers only the 217 held-out commune-years that were declared; it says nothing about dwellings in undeclared communes that never reached an insurer's ledger. The four insurers, with roughly one third of the market between them, are also a selected sample, and the register does not show how their portfolios differ from those of the other insurers.

Property-level and monthly records would improve both models more than any change of algorithm, and the frequency model is already a usable basis for the provision that the Secretariat requires, one that other compulsory covers paying only after a declaration could adopt in the same form.